Optimal harvesting policy for an age-structured predator–prey model with herd behavior

In this paper, we consider a more realistic predator–prey model where the predator has age structure and the prey exhibits herd behavior to defend against predators. The optimal harvesting, age structure and herd behavior are considered at the same time in the paper, which is our innovative point. First, we prove the existence and uniqueness of the non-negative solution for this model. Then, the optimal harvesting policy is derived by searching the extremum point of the cost functional. Furthermore, the existence of a unique optimal harvesting strategy is demonstrated by Ekeland’s Principle. Finally, numerical simulations show that seasonal harvesting is indeed necessary in real life to promote biological resource recovery.